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Question -

In the figure, common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.



Answer -

Given : Two common tangents PQ and RS intersect each other at A.
To prove : PQ = RS
Proof: From A, AQ and AR are two tangents are drawn to the circle with centre O.
 
AP = AR ….(i)
Similarly AQ and AS are the tangents to the circle with centre C
AQ = AS ….(ii)
Adding (i) and (ii)
AP + AQ = AR + AS
=> PQ = RS
Hence proved.

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